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The “Lower Town” archaeological site in Mycenae, Argolis, Greece has been excavated since 2007 and multiple periods of occupation and abandonment are represented in the stratigraphy uncovered. Sedimentary deposits were grouped into two general categories during excavation and these categories shaped fieldwork decisions: yellow-orange sediment with denser artifact concentrations representing potential occupation and red sediment with sparser artifacts representing abandonment. The distributions of point locations of artifacts within these bodies of sediment are analyzed statistically for spatial homogeneity using Ripley’s K in a GIS environment to test these site formation assumptions. Statistically significant spatial clustering in artifacts is assumed for autochthonous occupation deposits. These analyses were designed to be used to explicitly test otherwise implicit assumptions during fieldwork in future fieldwork. Results are mixed, with several factors complicating the interpretation of results without the hindsight of postieldwork artifactual and geoarchaeological analyses.

In the face of spatially correlated data, Gaussian process regression is a very common modeling approach. Given observational data, kriging equations will provide the best linear unbiased predictor for the mean at unobserved locations. However, when a computer model provides a complete grid of forecasted values, kriging will not apply. To develop an approach to quantify uncertainty of computer model output in this setting, we leverage information from a collection of computer model runs (e.g., historical forecast and observation pairs for tropical cyclone precipitation totals) through a Bayesian hierarchical framework. This framework allows us to combine information and account for the spatial correlation within and across computer model output. Using maximum likelihood estimates and the corresponding Hessian matrices for Gaussian process parameters, these are input to a Gibbs sampler which provides posterior distributions for parameters of interest. These samples are used to generate predictions which provide uncertainty quantification for a given computer model run (e.g., tropical cyclone precipitation forecast). We then extend this framework using deep Gaussian processes to allow for nonstationary covariance structure, applied to multiple computer model runs from a cosmology application. We also perform sensitivity analyses to understand which parameter inputs most greatly impact cosmological computer model output. / Doctor of Philosophy / A crucial theme when analyzing spatial data is that locations that are closer together are more likely to have similar output values (for example, daily precipitation totals). For a particular event, common modeling approach of spatial data is to observe data at numerous locations, and make predictions for locations that were unobserved. In this work, we extend this within-event modeling approach by additionally learning about the uncertainty across different events. Through this extension, we are able to quantify uncertainty for a particular computer model (which may be modeling tropical cyclone precipitation, for example) that does not provide any uncertainty on its own. This framework can be utilized to quantify uncertainty across a vast array of computer model outputs where more than one event or model run has been obtained. We also study how inputting different values into a computer model can influence the values it produces.

This dissertation investigates environmental degradation of a wetland ecosystem in the northeast Peruvian Amazon: the palm swamps, or aguajales, mostly located in the region of Loreto, Peru. This ecosystem is dominated by the dioecious palm species Mauritia flexuosa, locally known as aguaje. Female aguaje palms produce a valuable fruit which is widely consumed in the region, and especially in the capital city Iquitos. The most common method of harvesting this fruit is to chop the female palms. Concern is growing over environmental degradation that results from this practice, such as high carbon emissions released from the peat soils upon which most aguajales grow. This dissertation investigates environmental degradation of the palm swamps from multiple scales. Using a mixed-methods analysis, this dissertation asks: 1) What is the magnitude and distribution of palm swamp degradation, and what is the contribution of this process to carbon emissions? 2) What is the relative influence of physical and social underlying drivers explaining the spatial distribution of palm swamp ecosystems with different palm swamp densities? 3) How do underlying social-ecological/political-ecological driving forces occurring at different scales influence the sustainable use and conservation of palm swamp ecosystems? Degradation is mapped at the regional scale using remote sensing techniques over two periods of time: 1990-2007 and 2007-2018. Underlying drivers of degradation are investigated at the regional and district levels using spatially explicit statistical models. Finally, qualitative data acquired in the field is used to investigate why some communities successfully manage their palm swamps while others do not. This dissertation produces the first regional map of palm swamp degradation and first temporal analysis of how degradation has changed over three decades. It is the first study to analyze both physical and socioeconomic drivers of degradation and the first study to analyze how physical drivers change over time. It contributes to the literature of land change science by demonstrating a method of testing socioeconomic data at an aggregated scale against degradation data derived from remote sensing. Finally, this study provides a detailed and nuanced analysis of the aguaje social-ecological system, demonstrating that the choice of some communities to chop palms for harvest is not one made of ignorance, but rather is a logical option in marginalized communities where the aguaje fruit cannot provide a sufficient contribution to a community’s material needs. This work contributes to the literature of critical conservation by demonstrating cases of conservation success that were achieved without coercive state power. / Accompanied by 1 PDF file: chap1.pdf

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Statistical process monitoring and hierarchical Bayesian modeling are two ways to learn more about processes of interest. In this work, we consider two main components: risk-adjusted monitoring and Bayesian hierarchical models for spatial data. Usually, if prior information about a process is known, it is important to incorporate this into the monitoring scheme. For example, when monitoring 30-day mortality rates after surgery, the pre-operative risk of patients based on health characteristics is often an indicator of how likely the surgery is to succeed. In these cases, risk-adjusted monitoring techniques are used. In this work, the practical limitations of the traditional implementation of risk-adjusted monitoring methods are discussed and an improved implementation is proposed. A method to perform spatial risk-adjustment based on exact locations of concurrent observations to account for spatial dependence is also described. Furthermore, the development of objective priors for fully Bayesian hierarchical models for areal data is explored for Gaussian responses. Collectively, these statistical methods serve as analytic tools to better monitor and model spatial processes. / Ph. D.

In this dissertation, we develop a model selection and estimation methodology for nonstationary spatial fields. Large, spatially correlated data often cover a vast geographical area. However, local spatial regions may have different mean and covariance structures. Our methodology accomplishes three goals: (1) cluster locations into small regions with distinct, stationary models, (2) perform Bayesian model selection within each cluster, and (3) correlate the model selection and estimation in nearby clusters. We utilize the Conditional Autoregressive (CAR) model and Ising distribution to provide intra-cluster correlation on the linear effects and model inclusion indicators, while modeling inter-cluster correlation with separate Gaussian processes. We apply our model selection methodology to a dataset involving the prediction of Brook trout presence in subwatersheds across Pennsylvania. We find that our methodology outperforms the stationary spatial model and that different regions in Pennsylvania are governed by separate Gaussian process regression models. / Ph. D.

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